In order to observe the mass range as large as possible, the frequency range in Eq. (REF ) between \(f_{\mathrm {min}}\)  and \(f_{\mathrm {max}}\)  should be large so that \(\mathrm {S/N} > 8\) . We set the \(f_{\mathrm {min}}\)  as the minimal detectable frequency of the detector. The \(f_{\mathrm {max}}\)  is set to the minimal quantity between the maximal detectable frequency of the detector and the maximal redshifted inspiral phase frequency \(f_{\mathrm {insp}}^{\mathrm {max}}/(1+z) \mathrm {Hz}\) . Here, the maximal inspiral phase frequency in rest frame can be estimated as \(f_{\mathrm {insp}}^{\mathrm {max}} = (a \eta ^2 + b \eta + c)/\pi G M\)  [1]}, [2]}, [3]}. The symmetric mass ratio \(\eta \)  is defined as \(\eta \equiv m_1 m_2/M^2\) , \(M \equiv m_1 + m_2\)  and the coefficients \(a=0.29740\) , \(b=0.04481\) , \(c=0.09556\)  (See Table 1 of [4]}). The \(S_n(f)\)  for each detector can be obtained from Fig. A2 in [5]}.
